分类： 数学

TEN SIMPLE RULES FOR MATHEMATICAL WRITING – 笔记

Ten Rules

  • Structure rules (break it into digestible pieces)
    • Organize in segments
    • Write segments linearly
    • Consider a hierarchical development
  • Consistency rules (be boring creatively)
    • Use consistent notation and nomenclature
    • State results consistently
    • Don’t underexplain – don’t overexplain
  • Readability rules (make it easy for the reader)
    • Tell them what you’ll tell them
    • Use suggestive references
    • Consider examples and counterexamples
    • Use visualization when possible

Interesting Rules

TELL THEM WHAT YOU’LL TELL THEM

  • Keep the reader informed about where you are and where you are going
  • Start each segment with a short introduction and perhaps a road map
  • Tell them what you told them

二项式反演

对称的反演

二项式反演的主要内容就是：

\[ f_n = \sum_{i = 0}^n (-1)^i {n \choose i} g_i \longleftrightarrow g_n = \sum_{i = 0}^n (-1)^i {n \choose i} f_i \]

这个反演的式子非常的优美：在这种形式下，它们是对称的。当然，亦可以写作：

\[ f_n = \sum_{i = 0}^n {n \choose i} g_i \longleftrightarrow g_n = \sum_{i = 0}^n (-1)^{n – i} {n \choose i} f_i \]

继续阅读二项式反演